Worksheets on Fractions and Whole Numbers in Grade 3

Master fractions and whole numbers: comparing, adding, subtracting, converting, and mixed number operations through these comprehensive worksheets.

Worksheets: Exercises 1 to 3
1 Understanding Fractions
Worksheet 1
Circle the fraction of the shape that is shaded. Then write the fraction in numbers.
1. A circle divided into 4 equal parts with 3 parts shaded
2. A rectangle divided into 6 equal parts with 2 parts shaded
3. A square divided into 8 equal parts with 5 parts shaded
Definition:

Fraction: A number that represents part of a whole

Numerator: The top number showing how many parts are taken

Denominator: The bottom number showing total equal parts

Fraction Identification Method:
  1. Count the total number of equal parts
  2. Count the number of shaded parts
  3. Write as numerator/denominator
3/4
5/8
Problem 1
3 out of 4
Fraction
3/4
Result
Three-fourths
Step 1: Identify the total parts

Circle divided into 4 equal parts

Step 2: Count the shaded parts

3 parts are shaded

Step 3: Write the fraction

Numerator = 3 (shaded parts), Denominator = 4 (total parts)

Fraction = 3/4

The fraction is 3/4
Answers:

1. 3/4 (Three-fourths)

2. 2/6 (Two-sixths), which simplifies to 1/3

3. 5/8 (Five-eighths)

Applied rules:

• Fraction Parts: Numerator/Denominator

• Equal Parts: The whole must be divided into equal parts

• Reading Fractions: Read numerator over denominator

2 Adding Fractions
Worksheet 2
Add the fractions with the same denominator:
1. 1/5 + 2/5
2. 3/8 + 1/8
3. 4/7 + 2/7
Definition:

Like Fractions: Fractions with the same denominator

Adding Fractions: Only add numerators when denominators are the same

1/5 + 2/5 = 3/5
Problem
1/5 + 2/5
Same Denominator
Yes
Result
3/5
Step 1: Check denominators

Both fractions have denominator 5 (same denominator)

Step 2: Add numerators

1 + 2 = 3

Step 3: Keep the same denominator

Denominator stays 5

Step 4: Write the answer

1/5 + 2/5 = 3/5

1/5 + 2/5 = 3/5
Answers:

1. 1/5 + 2/5 = 3/5

2. 3/8 + 1/8 = 4/8 = 1/2

3. 4/7 + 2/7 = 6/7

Applied rules:

• Same Denominator: Only add when denominators match

• Add Numerators: Keep denominator the same

• Simplification: Reduce to lowest terms when possible

3 Comparing Fractions
Worksheet 3
Compare the fractions using >, <, or =:
1. 2/3 _____ 1/3
2. 3/4 _____ 3/5
3. 1/2 _____ 2/4
Definition:

Comparing Fractions: Determining which fraction is larger, smaller, or equal

Like Denominators: Compare numerators directly

Like Numerators: Compare denominators inversely

2/3
1/3
Problem
2/3 vs 1/3
Same Denominator
Yes
Result
2/3 > 1/3
Step 1: Check denominators

Both fractions have denominator 3 (same denominator)

Step 2: Compare numerators

2 > 1, so 2/3 > 1/3

Step 3: Write the comparison

2/3 > 1/3

2/3 > 1/3
Answers:

1. 2/3 > 1/3

2. 3/4 > 3/5 (same numerators, smaller denominator is larger)

3. 1/2 = 2/4 (equivalent fractions)

Applied rules:

• Same Denominator: Larger numerator = larger fraction

• Same Numerator: Smaller denominator = larger fraction

• Equivalent Fractions: Different names for same amount

Fractions and Whole Numbers: Rules and Methods
Fraction = Part/Whole
Fraction Representation
a/b + c/b = (a+c)/b
Adding Like Fractions
Definition
Fraction
Part of a whole
Numerator
Top Number
Parts taken
Denominator
Bottom Number
Total parts
Mixed Number
Whole + Fraction
1½, 2¾
Key definitions:

Fraction: A number representing part of a whole (numerator/denominator)

Whole Number: A number without fractions (0, 1, 2, 3...)

Improper Fraction: Numerator ≥ denominator (5/4, 7/3)

Mixed Number: Whole number + proper fraction (1½, 2¾)

Complete methodology:
  1. Identify the operation: Add, subtract, compare, convert
  2. Check denominators: Same or different?
  3. Apply appropriate rule: Based on operation and denominators
  4. Calculate: Perform the arithmetic
  5. Simplify: Reduce to lowest terms when possible
Tip 1: Use visual models (circles, bars) to understand fractions better.
Tip 2: When denominators are the same, only compare or add numerators.
Tip 3: The larger the denominator, the smaller each piece becomes.
Tip 4: Equivalent fractions represent the same amount (1/2 = 2/4 = 4/8).
Common errors: Adding denominators, forgetting to keep denominators the same, misidentifying equivalent fractions.
Exam preparation: Practice with visual models, memorize equivalencies, work on word problems.
Formulas to know by heart:

• Adding like fractions: a/b + c/b = (a+c)/b

• Converting mixed to improper: Whole × Denominator + Numerator

• Converting improper to mixed: Divide numerator by denominator

• Equivalent fractions: Multiply/divide both parts by same number

Worksheets: Exercises 4 to 5
4 Converting Mixed Numbers
Worksheet 4
Convert mixed numbers to improper fractions:
1. 2½
2. 3¾
3. 1⅔
Definition:

Mixed Number: A whole number combined with a proper fraction

Improper Fraction: A fraction where numerator ≥ denominator

2½
→
5/2
(5 halves)
Mixed Number
2½
Conversion
2×2+1=5
Result
5/2
Step 1: Multiply whole number by denominator

2 × 2 = 4

Step 2: Add the numerator

4 + 1 = 5

Step 3: Keep the same denominator

Denominator stays 2

Step 4: Write the improper fraction

2½ = 5/2

2½ = 5/2
Answers:

1. 2½ = 5/2

2. 3¾ = 15/4

3. 1⅔ = 5/3

Applied rules:

• Mixed to Improper: (Whole × Denominator) + Numerator

• Keep Denominator: The denominator stays the same

• Visual Thinking: Count total pieces in the model

5 Word Problems
Worksheet 5
Solve these fraction word problems:
1. Sarah ate 1/4 of a pizza. Her brother ate 2/4 of the same pizza. How much pizza did they eat altogether?
2. Tom had 3½ cups of flour. He used 1¼ cups for baking. How much flour does he have left?
Definition:

Word Problems: Real-life situations requiring fraction operations

Problem Solving: Identifying operations needed to solve problems

Pizza Problem
1/4 + 2/4 = 3/4
Problem 1
1/4 + 2/4
Operation
Addition
Result
3/4
Step 1: Identify the operation needed

"How much altogether?" indicates addition

Step 2: Check denominators

Both fractions have denominator 4 (same denominator)

Step 3: Add the numerators

1 + 2 = 3

Step 4: Keep the same denominator

Denominator stays 4

They ate 3/4 of the pizza
Answers:

1. 1/4 + 2/4 = 3/4 of the pizza eaten

2. 3½ - 1¼ = 2¼ cups of flour left

Applied rules:

• Keywords: "altogether" = addition, "left" = subtraction

• Same Denominators: Add or subtract numerators only

• Real-World Context: Connect math to practical situations

Comprehensive Summary: Fractions and Whole Numbers
a/b = a ÷ b
Fraction as Division
Complete definitions:

Fraction: A number representing part of a whole, written as numerator/denominator

Proper Fraction: Numerator < denominator (less than 1, like 3/4)

Improper Fraction: Numerator ≥ denominator (equal to or greater than 1, like 5/4)

Mixed Number: Combination of whole number and proper fraction (like 1½)

Equivalent Fractions: Different fractions representing the same value (1/2 = 2/4)

Like Fractions: Fractions with the same denominator (3/5 and 1/5)

Unlike Fractions: Fractions with different denominators (1/3 and 1/4)

Complete methodologies:

Adding/Subtracting Like Fractions:

  1. Keep the same denominator
  2. Add/subtract numerators only
  3. Simplify if possible

Converting Mixed Numbers:

  1. Mixed to Improper: (Whole × Denominator) + Numerator
  2. Improper to Mixed: Divide numerator by denominator

Comparing Fractions:

  1. Same denominator: Compare numerators
  2. Same numerator: Compare denominators (larger denominator = smaller fraction)
  3. Different: Find common denominator or convert to decimals
Memorization Tip: "Denominator" is down below (bottom), "Numerator" is up above (top).
Visualization: Think of fractions as pieces of a pie or parts of a whole bar.
Equivalent Fractions: Multiply or divide both numerator and denominator by the same number.
Common Denominator: Needed for adding/subtracting unlike fractions (not covered in grade 3).
Common Mistakes: Adding denominators instead of keeping them, forgetting to simplify, confusing numerators and denominators.
Key Applications: Cooking, measuring, sharing items, time, money, and geometric shapes.
Essential rules to memorize:

• Fraction Structure: Numerator (parts taken) / Denominator (total parts)

• Adding Like Fractions: a/b + c/b = (a+c)/b

• Subtracting Like Fractions: a/b - c/b = (a-c)/b

• Mixed Number Conversion: Whole × Denominator + Numerator

• Comparison Rules: Same denominator → compare numerators; Same numerator → compare denominators

Problem-solving strategies:

• Read the problem carefully and identify key words

• Draw a visual model to represent the situation

• Determine which operation is needed

• Check if denominators are the same

• Perform the calculation and simplify if needed

• Verify your answer makes sense in the context of the problem

Questions & Answers

Question: I don't understand why 1/2 and 2/4 are the same amount. Can you explain?

Answer: Great question! These are called equivalent fractions because they represent the same portion of a whole:

  • If you cut a pizza in half (2 pieces) and take 1 piece, you have 1/2 of the pizza
  • If you cut the same pizza into 4 pieces and take 2 pieces, you also have 1/2 of the pizza

To find equivalent fractions, multiply or divide both numerator and denominator by the same number:

1/2 = (1×2)/(2×2) = 2/4

This is why 1/2 and 2/4 represent the same amount!

Question: My child gets confused when adding fractions. How can I help them remember the rules?

Answer: Here are helpful strategies for adding fractions:

  • First, check if denominators are the same (like fractions)
  • If yes, add only the numerators and keep the denominator
  • If no, you need to learn about common denominators (in higher grades)

Use visual aids like fraction circles or bars to show the concept concretely.

Remember: "DENOMINATOR stays the SAME, NUMERATOR gets added!"

Question: What does it mean when a fraction has a bigger number on top than on bottom?

Answer: When the top number (numerator) is bigger than the bottom number (denominator), it's called an improper fraction!

Example: 5/3 means you have 5 parts when each whole has only 3 parts. This is more than one whole!

You can convert improper fractions to mixed numbers: 5/3 = 1⅔ (one whole and two-thirds).

Think of it like having more slices of pizza than fit in one whole pizza!